Supported networks for Verizon 5S...

This year I am kinda confused...anyways...I have a Verizon model and I put my friends AT&T sim in my phone to see if its unlocked and BAM AT&T LTE pops up quick...I do know the Verizon model iPhone 5 worked with HSPA+ last year so that was a nice surprise..so it working with AT&T's network completely was a GREAT surprise...it will make selling it next year before I get the new iPhone model next year much easier. But anyways...would this phone work with AT&T's HSPA+ (and international I'd assume) network? Does it work with Sprint's 3G and LTE band (Band 25), and would it work with T-Mobile's AWS HSPA+ and LTE network??? (American T-Mobile I mean)

This year I am kinda confused...anyways...I have a Verizon model and I put my friends AT&T sim in my phone to see if its unlocked and BAM AT&T LTE pops up quick...I do know the Verizon model iPhone 5 worked with HSPA+ last year so that was a nice surprise..so it working with AT&T's network completely was a GREAT surprise...it will make selling it next year before I get the new iPhone model next year much easier. But anyways...would this phone work with AT&T's HSPA+ (and international I'd assume) network? Does it work with Sprint's 3G and LTE band (Band 25), and would it work with T-Mobile's AWS HSPA+ and LTE network??? (American T-Mobile I mean)